A vibration damper to which a clamp-shaped attachment part is fastened is known from DE 10 2009 001 256 A1. The vibration damper comprises a cylinder with a circular cross section. The clamp-shaped attachment part is arranged on a lateral surface of the cylinder. In unclamped condition of the attachment part, two radial tabs form a gap with an acute angle. When a predetermined clamping force is applied by means of clamping screws, the two tabs move together so that the angle decreases. In a tubular body of the attachment part, a clamping is applied in circumferential direction of the tubular body by this clamping movement of the tabs. This clamping provides for a retaining force of the attachment part at the cylinder. An additional expansion of the diameter of the cylinder for axial support of the attachment part is unnecessary in this case.
A basic problem exists in that the uneven clamping distribution between tubular body and cylinder leads to clamping peaks which may exceed strength values of the cylinder in some cases.